The rook and the bishop are moving independently on the chessboard starting at the same corner
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The rook and the bishop are moving independently on the chessboard starting at the same corner. What is the average number of steps until they meet again in the same corner, if we know that the bishop moves only on one quarter of the chessboard?
I suppose that I should use Markov chains / processes. I think that I should consider two transition matrices: one 8x8 and one 4x4, and then model a proper graph. We need to find the probability that those 2 figures meet in the same time and in the same spot, not only the probability of getting back to the corner. I'm new to this subject, so please be indulgent. Any help or tips will be much appreciated.
probability-theory stochastic-processes markov-chains random-walk
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
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|
show 3 more comments
$begingroup$
The rook and the bishop are moving independently on the chessboard starting at the same corner. What is the average number of steps until they meet again in the same corner, if we know that the bishop moves only on one quarter of the chessboard?
I suppose that I should use Markov chains / processes. I think that I should consider two transition matrices: one 8x8 and one 4x4, and then model a proper graph. We need to find the probability that those 2 figures meet in the same time and in the same spot, not only the probability of getting back to the corner. I'm new to this subject, so please be indulgent. Any help or tips will be much appreciated.
probability-theory stochastic-processes markov-chains random-walk
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
$endgroup$
2
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
1
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
1
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
1
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08
|
show 3 more comments
$begingroup$
The rook and the bishop are moving independently on the chessboard starting at the same corner. What is the average number of steps until they meet again in the same corner, if we know that the bishop moves only on one quarter of the chessboard?
I suppose that I should use Markov chains / processes. I think that I should consider two transition matrices: one 8x8 and one 4x4, and then model a proper graph. We need to find the probability that those 2 figures meet in the same time and in the same spot, not only the probability of getting back to the corner. I'm new to this subject, so please be indulgent. Any help or tips will be much appreciated.
probability-theory stochastic-processes markov-chains random-walk
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
$endgroup$
The rook and the bishop are moving independently on the chessboard starting at the same corner. What is the average number of steps until they meet again in the same corner, if we know that the bishop moves only on one quarter of the chessboard?
I suppose that I should use Markov chains / processes. I think that I should consider two transition matrices: one 8x8 and one 4x4, and then model a proper graph. We need to find the probability that those 2 figures meet in the same time and in the same spot, not only the probability of getting back to the corner. I'm new to this subject, so please be indulgent. Any help or tips will be much appreciated.
probability-theory stochastic-processes markov-chains random-walk
probability-theory stochastic-processes markov-chains random-walk
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
asked Dec 22 '18 at 17:06
MacAbraMacAbra
267210
267210
2
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
1
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
1
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
1
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08
|
show 3 more comments
2
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
1
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
1
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
1
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08
2
2
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
1
1
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
1
1
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
1
1
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08
|
show 3 more comments
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2
$begingroup$
How far do the pieces move when they move? With what probabilities do they move?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:08
$begingroup$
@kimchilover There's no such an information in my exercise
$endgroup$
– MacAbra
Dec 22 '18 at 17:09
1
$begingroup$
Pity. Maybe previous exercises give hints that will let you formulate your exercise with enough precision to admit an answer?
$endgroup$
– kimchi lover
Dec 22 '18 at 17:12
1
$begingroup$
So make up some plausible scenario and edit it into your question. Such as, each piece picks any legal move with uniform probability.
$endgroup$
– kimchi lover
Dec 22 '18 at 17:33
1
$begingroup$
What does it mean "the bishop moves only on one quarter of the chessboard"?
$endgroup$
– MJD
Dec 22 '18 at 18:08